Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Second Derivative of Determinant of Matrix?

  1. Dec 31, 2011 #1
    Hi all....

    I've read on wikipedia (facepalm) that the first derivative of a determinant is

    del(det(A))/del(A_ij) = det(A)*(inv(A))_j,i

    If we go to find the second derivative (applying power rule), we get:

    del^2(A) / (del(A)_pq) (del (A)_ij) = {del(det(A))/del(A_pq)}*(inv(A))_j,i + det(A)*{del(inv(A)_j,i) / del(A_pq)}

    I have no clue how to calculate the derivative of the inverse of a matrix with respect to changing the values in the original matrix:
    I.E. del(inv(A)_j,i) / del(A_pq)

    Also.... would be nice if someone could prove the first statement for the first derivative of the determinant.

  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?